Towards automated homomorphic encryption parameter selection with fuzzy logic and linear programming.

Homomorphic Encryption (HE) is a set of powerful properties of certain cryptosystems that allow privacy-preserving operation over the encrypted text. Still, HE is not widespread due to limitations in terms of efficiency and usability. Among the challenges of HE, scheme parametrization (i.e., the selection of appropriate parameters within the algorithms) is a relevant multi-faced problem. First, the parametrization needs to comply with a set of properties to guarantee the security of the underlying scheme. Second, parametrization requires a deep understanding of the low-level primitives since the parameters have a confronting impact on the scheme's precision, performance, and security. Finally, the circuit to be executed influences, and it is influenced by, the parametrization. Thus, there is no general optimal selection of parameters, and this selection depends on the circuit and the scenario of the application. Currently, most existing HE frameworks require cryptographers to address these considerations manually. It requires a minimum of expertise acquired through a steep learning curve. In this paper, we propose a unified solution for the aforementioned challenges. Concretely, we present an expert system combining Fuzzy Logic and Linear Programming. The Fuzzy Logic Modules receive a user selection of high-level priorities for the security, efficiency, and performance of the cryptosystem. Based on these preferences, the expert system generates a Linear Programming Model that obtains optimal combinations of parameters by considering those priorities while preserving a minimum level of security for the cryptosystem. We conduct an extended evaluation showing that an expert system generates optimal parameter selections that maintain user preferences without undergoing the inherent complexity of analyzing the circuit. • Homomorphic Encryption scheme parametrization is a complex procedure. • Scheme parametrizations can be represented as Linear Programming Tasks. • Fuzzy Logic loosens the constraints of the Linear Programming Task. • Together Fuzzy Logic and Linear Programming provide near-optimal parametrizations. • The parametrization complexity is reduced and couples with user preferences. [ABSTRACT FROM AUTHOR]